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3. Use the U.S. Treasury Yield Curve for 9/4/2020 given below. You can use this to estimate the average rate of inflation for the next thirty years as the difference between the nominal rate on a 30-Year Treasury bond and the Inflation Indexed Treasury bond-(often called Treasury Inflation Protected bonds or TIPs-Real Rate). Also, the shape of the Yield Curve also tells us something about future interest rates. US Treasury Yield Curve 9/4/2020 U.S. Treasury Nominal Yield Curve Date 1 Mo 2 Mo 3 Mo 6 Mo 1 Yr 2 Yr 3 Yr 5 Yr 7 Yr 10 Yr 20 Yr 30 Yr 9/4/20 0.09 0.10 0.11 0.12 0.13 0.14 0.18 0.30 0.50 0.72 1.46 1.25 https://www.treasurv.cov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data vield U.S. Treasury Real Yield Curve DATE 5YR 7 YR 10 YR 20 YR 30 YR 9/4/20 -1.27 -1.15-0.98 -0.59-0.33 https://www.treasury.com/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=realvield Your 28 year old client wants to retire when he is 70 years old with a retirement income equivalent to $8,000 per month in today's dollars. To estimate the market expectations for average annual inflation for the next 42 years, use the difference between the 30-year US Treasury nominal rate and 30-year US Treasury real rate (rate on TIPs). Because of inflation, your client will need substantially higher retirement monthly income to maintain the same purchasing power. He plans to purchase a guaranteed lifetime annuity from an insurance company one month before he retires (503 months from now). The retirement annuity will begin in exactly 42 years (504 months). At the time the retirement annuity is purchased, the insurance company will add a 5.00 percent premium to the pure premium cost of the purchase price of the annuity. The pure premium is the actuarial cost to the insurance company of his anticipated lifetime annuity. He has savings of $80,000 today that will be invested at an annual return of 6.00% but compounded monthly. Given a rate of return of 6.00% for the foreseeable future for both himself and the insurance company that he plans to purchase the guaranteed life time annuity from, how much does he need to save each month (total of 503 payments) until the month before he retires? He will make the first payment next month and the last payment one month before he retires. For life expectancy after retirement at age 70, use the Cohort Life Tables for Social Security Area by Sex table below: Cohort Life Tables for Social Security by Sex Male Female Probability W of 100,000 Life Probability Age Death Living Expectancy Age Death 40 0.00170 96,759 42.94 40 0.00108 0.00183 96,595 42.01 0.00116 42 0.00196 96,418 41.09 0.00123 43 0.00209 96,229 40.17 0.00129 44 0.00223 96,028 39.25 0.00135 45 0.00238 95,814 38.33 45 0.00142 46 0.00254 95,586 37.43 0.00150 47 0.00268 95,343 36.52 47 0.00159 48 0.00278 95,088 35.62 0.00168 49 0.00288 94,823 34.71 49 0.00178 50 0.00299 94.550 33.81 50 0.00190 51 0.00313 94,268 32.91 S1 0.00204 52 0.00331 93.973 32.01 52 0.00221 53 0.00355 93,662 31.12 53 0.00241 54 0.00385 93.329 30.23 54 0.00265 55 0.00419 92,970 29.34 55 0.00292 56 0.00457 92,581 28.46 56 0.00322 57 0.00497 92,158 27.59 57 0.00354 58 0.00539 91,700 26.73 58 0.00386 59 0.00585 91,205 25.87 59 0.00420 60 0.00635 90,672 25.02 60 0.00457 61 0.00693 90,096 24.18 61 0.00500 0.00763 89,472 23.34 0.00551 63 0.00847 88,790 22.52 0.00613 64 0.00944 88,038 21.70 0.00683 65 0.01053 87.206 20.91 65 0.00762 66 0.01167 86,288 20.12 66 0.00845 67 0.01284 85,281 19.36 0.00930 68 0.01402 84,186 18,60 0.01014 69 0.01523 83,006 17.86 69 0.01101 70 0.01660 81,742 17.13 70 0.01199 71 0.01811 80,385 16.41 71 0.01308 72 0.01965 78,929 15.70 72 0.01419 73 0.02119 77,378 15.01 73 0.01533 74 0.02280 75,739 14.32 74 0.01653 75 0.02479 74,012 13.64 75 0.01804 of 100.000 Life Living Expectancy 98,088 46.22 97,982 45.27 97,869 44.33 97,749 43.38 97,622 42.43 97.490 41.49 97,352 40.55 97.205 39.61 97,051 38.67 96.888 37.74 96,715 36.80 96.532 35.87 96,335 34.94 96,123 34.02 95.891 33.10 95.637 32.19 95.358 31.28 95,051 30.38 94,714 29.49 94348 28.60 93.952 27.72 93.522 26.84 93,054 25.97 92.541 25.12 91,974 24.27 91.346 23.43 90.650 22.61 89.884 21.80 89.048 21.00 88,145 20:21 87,175 19.42 86,130 18.65 85.003 17.89 83.797 17.15 82.513 16.40 $1,148 15.67 14.95 76 77 78 0.02713 0.02954 0.03200 72,177 70,219 68,144 65.964 12.98 12.32 11.68 11.05 76 77 78 0.01979 0.02154 0.02321 0.02502 79.685 78,107 76.425 74.651 14.24 13.54 12.85 79 0.03469 79 Expected Inflation = Expected Remaining Life in Months at Retirement = Needed per month retirement income (assume annual compounding). FV 42 years = $8,000 (1. )42 = $8,000 = $ Calculation of Total amount Needed in retirement account one month (month 503) before retirement. PVA, vorth, 503 = $ 1 (1 0. 0. = S $ 5% Premium and Insurance Company total price Price = (1.050) = Value of Current Savings in 503 months (assuming monthly compounding. FV 503 months = $80,000 (1. )503 = $80,000 s Total New Additional Saving needed by month 503 = *$ Saving Each month for next 503 Months. (1 m)* 1 FVA A 1 Then, A = *$ A Il per month
